English
Push forward a CommGroupWithZero along a surjective function.
Русский
Перемещение CommGroupWithZero вдоль сюръективной функции.
LaTeX
$$$\\text{CommGroupWithZero } M_0' = \\text{ pushforward along } f$$$
Lean4
/-- Push forward a `CommGroupWithZero` along a surjective function.
See note [reducible non-instances]. -/
protected def commGroupWithZero [Zero G₀'] [Mul G₀'] [One G₀'] [Inv G₀'] [Div G₀'] [Pow G₀' ℕ] [Pow G₀' ℤ]
(h01 : (0 : G₀') ≠ 1) (f : G₀ → G₀') (hf : Surjective f) (zero : f 0 = 0) (one : f 1 = 1)
(mul : ∀ x y, f (x * y) = f x * f y) (inv : ∀ x, f x⁻¹ = (f x)⁻¹) (div : ∀ x y, f (x / y) = f x / f y)
(npow : ∀ (x) (n : ℕ), f (x ^ n) = f x ^ n) (zpow : ∀ (x) (n : ℤ), f (x ^ n) = f x ^ n) : CommGroupWithZero G₀' :=
{ hf.groupWithZero h01 f zero one mul inv div npow zpow, hf.commSemigroup f mul with }
